10. When $3 g^{2}-4 g+2$ is subtracted from $7 g^{2}+5 g-1$, the difference is:

Step 1 ：Given two polynomials $7 g^{2}+5 g-1$ and $3 g^{2}-4 g+2$

Step 2 ：We need to subtract the second polynomial from the first one. This involves subtracting the coefficients of the like terms.

Step 3 ：The like terms are those terms which have the same variable and power. In this case, the like terms are $7g^2$ and $3g^2$, $5g$ and $-4g$, and $-1$ and $2$.

Step 4 ：We subtract the coefficients of these like terms separately and then combine them to get the final polynomial.

Step 5 ：The difference between the coefficients of $g^2$ is 4, the difference between the coefficients of $g$ is 9, and the difference between the constant terms is -3.

Step 6 ：Therefore, the difference between the two polynomials is $4g^2 + 9g - 3$.

Step 7 ：\(\boxed{4g^2 + 9g - 3}\) is the final answer.